Hi BadenBaden,
If you travel from Gatwick to London and then jaunt around zones 1-2 then the most you’ll pay is the zone 1-2 cap (£8.10) plus the single fare from Gatwick. So £17.60. It might be fractionally lower, but that’s the most.
If you haven’t got much luggage and don’t mind going up and down a ramp at East Croydon then that can be reduced to Gatwick to East Croydon* £3.70, zone 3-5 extension* £3.00 and the zone 1-2 cap of £8.10, total £14.80. You just need to get out at East Croydon, touch out and back in again, then get the next train to London. *Note that slightly higher fares apply between 1600-1900 from Gatwick.